why .stl-model in blender differ from .stl-model in makerware?
That is the result of non-planar faces.  STL files only support tris (partly for this exact reason).  So when you export a mesh to .stl, Blender will automatically triangulate all faces.  So if a face's vertices are only slightly non-coplanar, in Blender it won't look strange, but once the model is triangulated you will definitely be able to see the extra edge placed across the face.

The solution is to either model in tris, or to manually make the non-planar faces planar.  The latter solution is probably your best bet now, though it is kind of ugly.

As a side note I noticed that some of your normals are inverted (the darker faces), this might cause problems if you are planning on 3D printing your model.  To fix this simply select the faces and hit Ctrl+F > invert normals.